Determine whether the variable?X?has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parameters?n?and?p. If it doesn't, explain why not.
(a)??X =?Number of days it snows this coming April in Winnipeg.
(b)? Weights of apples sold in a grocery store follow a normal distribution with mean 150 grams and standard deviation 20 grams.? You take a random sample of five apples.
???????X?= number of apples heavier than 175 grams.
(c)? You randomly select a seven-digit phone number from the Winnipeg phone book (excluding area code).
????? ?X?= number of zeroes in the phone number.
(d)? The number of goals scored by the Winnipeg Jets follows a Poisson distribution with a rate of 2.6 per game.? We take a random sample of ten Jets games.
???? ??X?= number of games in which the Jets are shutout (i.e., they score zero goals).
The remainder of the questions refer to the following:
Suppose we have three boxes, each containing a number of coloured balls:
- ?Box 1 contains 5 red balls, 3 yellow balls and 2 green balls.
- ?Box 2 contains?9 red balls, 6 yellow balls and 5 green balls.
- ?Box 3 contains 14 red balls, 9 yellow balls and 7 green balls.
(e)? You randomly select 5 balls from Box 1 with replacement.
Determine whether the variable X has a binomial distribution in each of the following cases.
If it does, explain why and determine the values of the parameters n and p. If it doesn't,
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